The present invention relates to vibrating finishing machines of the type having an annular tub adapted to hold parts being treated and a finishing medium. The tub is vibrated by means of a rotary shaft carrying two eccentric weights. The present invention more particularly relates to the construction of a weight for use in such vibrating finishing machines such that the center of gravity of the weight is automatically displaced relative to the center of gravity of a fixed eccentric weight when the direction of rotation of the shaft is reversed.